Reducing unwanted vibrations or oscillations is a major concern for many systems including those as complex as the Remote Manipulator System used on the space shuttle as well as more mundane systems, e.g., the systems used to move the printhead cover in an inkjet printer. Attempts to improve system performance have included providing command inputs designed to reduce residual vibration after moves in the systems. Many command input schemes can, however, suffer from a lack of robustness. As used in connection with the present invention, "robustness" is the ability of the system, in response to the command input, to complete a motion or other output response without excessive residual oscillation/vibration in spite of changes in the system natural frequency.
In any system, it may be desirable to complete a move without residual vibrations when the governing criteria are one or more of (a) robustness, (b) minimum move time, and (c) minimum noise. In some instances, it would be desirable to enhance all of these characteristics, while in others it may be possible to focus on one or two of the characteristics.
Posicast control (O. J. M. Smith 1958) was an early attempt to cancel vibration in flexible systems by breaking the input step into two smaller steps to cancel vibration. This method, however, was not robust with respect to changes in the natural frequency of the system. Shaped torque techniques (Swigert 1980) were developed by using cost functions, but they also lacked robustness properties to system changes. Sehitoglu and Aristizabul (1986) used cycloidal motion profiles, but they had limited success.
More recently, robustness was addressed by a technique as described in U.S. Pat. No. 4,916,635 to Singer et al. Their four-impulse method, however, has a limited robustness range of about -30% to +40% for overshoot levels less than 5%. Furthermore this technique requires an approximate system model that includes every mode to be controlled. In addition, the method requires extra impulses which lengthens the move time.
Most recently, Kenjo and Sugawara (1994) have shown in their book a method called back-phasing which is used in stepper motors to cancel rotor oscillation, but which also lacks robustness. Others have developed feedback control techniques (Chen and Paden 1993) but these methods often require a detailed system model and additional feedback circuitry and hardware.
U.S. Pat. No. 5,594,309 (McConnell et al.) disclose another control method that exhibits increased robustness for systems having a wide spread between the fundamental and second natural frequencies.
In spite of the above attempts at providing robust control methods, a need exists for methods and systems that can supply robust command inputs that can be used to improve system performance in robustness, noise and/or speed as desired by the user.